Related papers: A Rapid Method For Orbital Coverage Statistics Wit…
In this paper, we investigate the performance of large-scale heterogeneous low Earth orbit (LEO) satellite networks in the context of three association schemes. In contrast to existing studies, where single-tier LEO satellite-based network…
Dense satellite constellations recently emerged as a prominent solution to complementing terrestrial networks in attaining true global coverage. As such, analytic optimization techniques can be adopted to rapidly maximize the benefits of…
We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random…
Consider $G=\SL_{ d }(\mathbb R)$ and $ \Gamma=\SL_{ d }(\mathbb Z)$. It was recently shown by the second-named author \cite{s} that for some diagonal subgroups $\{g_t\}\subset G$ and unipotent subgroups $U\subset G$, $g_t$-trajectories of…
This paper investigates the maximum achievable downlink spectral efficiency of low Earth orbit (LEO) satellite constellations. Spectral efficiency is defined here as the total network sum rate per unit bandwidth per unit area of Earth's…
We reexamine non-Einsteinian effects observable in the orbital motion of low-orbit artificial Earth satellites. The motivations for doing so are twofold: (i) recent theoretical studies suggest that the correct theory of gravity might…
We present the results of a study that uses numerical simulations to interpret observations of tidally disturbed satellites around the Milky Way. When analysing the simulations from the viewpoint of an observer, we find a break in the slope…
Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating…
As periodic orbit theory works badly on computing the observable averages of dynamical systems with intermittency, we propose a scheme to cooperate with cycle expansion and perturbation theory so that we can deal with intermittent systems…
Current theoretical studies on IoT-over-LEO satellite systems often rely on unrealistic assumptions, such as infinite terrestrial areas and omnidirectional satellite coverage, leaving significant gaps in theoretical analysis for more…
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…
We consider the use of multiple co-located satellites to improve the spectral efficiency of broadcast transmissions. In particular, we assume that two satellites transmit on overlapping geographical coverage areas, with overlapping…
We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional $S_{BG}[p(x)]…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
Given their extensive geographic coverage, low Earth orbit (LEO) satellites are envisioned to find their way into next-generation (6G) wireless communications. This paper explores space-air-ground integrated networks (SAGINs) leveraging…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
The distribution and the comparison of an ultra-stable optical frequency and accurate time using optical fibres have been greatly improved in the last ten years. The frequency stability and accuracy of optical links surpass well-established…
Recently, stochastic geometry has been applied to provide tractable performance analysis for low earth orbit (LEO) satellite networks. However, existing works mainly focus on analyzing the ``coverage probability'', which provides limited…